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Erschienen in: Mathematics and Financial Economics 1/2015

01.01.2015

An explicit analytic formula for pricing barrier options with regime switching

verfasst von: Leunglung Chan, Song-Ping Zhu

Erschienen in: Mathematics and Financial Economics | Ausgabe 1/2015

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Abstract

This paper investigates the valuation of a European-style barrier option in a Markovian, regime-switching, Black–Scholes–Merton economy, where the price process of an underlying risky asset is assumed to follow a Markov-modulated geometric Brownian motion. An explicit analytic solution in infinite series form for the price of a European-style barrier option in a two-state regime is presented.

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Literatur
1.
Zurück zum Zitat Baran, N.A., Yin, G., Zhu, C.: Feynman–Kac formula for switching diffusions: connections of systems of partial differential equations and stochastic differential equations. Adv.Differ. Equ. 315, 1–13 (2013) Baran, N.A., Yin, G., Zhu, C.: Feynman–Kac formula for switching diffusions: connections of systems of partial differential equations and stochastic differential equations. Adv.Differ. Equ. 315, 1–13 (2013)
2.
Zurück zum Zitat Black, F., Scholes, M.: The pricing of options and corporate liabilities. J. Polit. Econ. 81, 637–659 (1973)CrossRefMATH Black, F., Scholes, M.: The pricing of options and corporate liabilities. J. Polit. Econ. 81, 637–659 (1973)CrossRefMATH
3.
Zurück zum Zitat Boyarchenko, S.I., Levendorskiǐ, S.Z.: Barrier options and touch-and-out options under regular Lévy processes of exponential type. Ann. Appl. Prob. 12(4), 1261–1298 (2002)CrossRefMATH Boyarchenko, S.I., Levendorskiǐ, S.Z.: Barrier options and touch-and-out options under regular Lévy processes of exponential type. Ann. Appl. Prob. 12(4), 1261–1298 (2002)CrossRefMATH
4.
Zurück zum Zitat Buffington, J., Elliott, R.J.: Regime switching and European options. In: Pasik-Duncan, B. (ed.) Stochastic theory and control. proceedings of a workshop, Lawerence, Kansas, pp. 73–81. Springer, Berlin (2002) Buffington, J., Elliott, R.J.: Regime switching and European options. In: Pasik-Duncan, B. (ed.) Stochastic theory and control. proceedings of a workshop, Lawerence, Kansas, pp. 73–81. Springer, Berlin (2002)
5.
Zurück zum Zitat Buffington, J., Elliott, R.J.: American options with regime switching. Int. J. Theor. Appl. Financ. 5, 497–514 (2002) Buffington, J., Elliott, R.J.: American options with regime switching. Int. J. Theor. Appl. Financ. 5, 497–514 (2002)
6.
Zurück zum Zitat Elliott, R.J., Aggoun, L., Moore, J.B.: Hidden Markov Models: Estimation and Control. Springer, Berlin (1994) Elliott, R.J., Aggoun, L., Moore, J.B.: Hidden Markov Models: Estimation and Control. Springer, Berlin (1994)
7.
Zurück zum Zitat Elliott, R.J., Chan, L., Siu, T.K.: Option pricing and esscher transform under regime switching. Ann. Financ. 1(4), 423–432 (2005)CrossRefMATH Elliott, R.J., Chan, L., Siu, T.K.: Option pricing and esscher transform under regime switching. Ann. Financ. 1(4), 423–432 (2005)CrossRefMATH
8.
Zurück zum Zitat Elliott, R.J., Chan, L., Siu, T.K.: Option valuation under a regime-switching constant elasticity of variance process. Appl. Math. Comput. 219(9), 4434–4443 (2013)CrossRefMathSciNet Elliott, R.J., Chan, L., Siu, T.K.: Option valuation under a regime-switching constant elasticity of variance process. Appl. Math. Comput. 219(9), 4434–4443 (2013)CrossRefMathSciNet
9.
Zurück zum Zitat Elliott, R.J., Siu, T.K., Chan, L.: On pricing barrier options with regime switching. J. Comput. Appl. Math. 256, 196–210 (2014)CrossRefMathSciNet Elliott, R.J., Siu, T.K., Chan, L.: On pricing barrier options with regime switching. J. Comput. Appl. Math. 256, 196–210 (2014)CrossRefMathSciNet
10.
Zurück zum Zitat Gounden, S., O’Hara, J.G.: An analytic formula for the price of an American-style Asian option of floating strike type. Appl. Math. Comput. 217, 2923–2936 (2010)CrossRefMATHMathSciNet Gounden, S., O’Hara, J.G.: An analytic formula for the price of an American-style Asian option of floating strike type. Appl. Math. Comput. 217, 2923–2936 (2010)CrossRefMATHMathSciNet
11.
Zurück zum Zitat Guo, X.: Information and option pricings. Quant. Financ. 1, 38–44 (2001)CrossRef Guo, X.: Information and option pricings. Quant. Financ. 1, 38–44 (2001)CrossRef
12.
13.
Zurück zum Zitat Kou, S.G., Wang, H.: Option pricing under a double exponential jump diffusion model. Manage. Sci. 50, 1178–1192 (2004)CrossRef Kou, S.G., Wang, H.: Option pricing under a double exponential jump diffusion model. Manage. Sci. 50, 1178–1192 (2004)CrossRef
14.
Zurück zum Zitat Leung, K.S.: An analytic pricing formula for lookback options under stochastic volatility. Appl. Math. Lett. 26, 145–149 (2013)CrossRefMATHMathSciNet Leung, K.S.: An analytic pricing formula for lookback options under stochastic volatility. Appl. Math. Lett. 26, 145–149 (2013)CrossRefMATHMathSciNet
15.
Zurück zum Zitat Liao, S.-J.: Numerically solving non-linear problems by the homotopy analysis method. Comput. Mech. 20, 530–540 (1997)CrossRefMATH Liao, S.-J.: Numerically solving non-linear problems by the homotopy analysis method. Comput. Mech. 20, 530–540 (1997)CrossRefMATH
16.
Zurück zum Zitat Liao, S.-J., Campo, A.: Analytic solutions of the temperature distribution in Blasius viscous flow problems. J. Fluid Mech. 453, 411–425 (2002)CrossRefMATHMathSciNet Liao, S.-J., Campo, A.: Analytic solutions of the temperature distribution in Blasius viscous flow problems. J. Fluid Mech. 453, 411–425 (2002)CrossRefMATHMathSciNet
17.
Zurück zum Zitat Liao, S.-J., Zhu, J.-M.: A short note on higher-order streamfunction-vorticity formulations of 2D steady state Navier–Stokes equations. Int. J. Numer. Meth. Fluids 22, 1–9 (1996)CrossRefMATH Liao, S.-J., Zhu, J.-M.: A short note on higher-order streamfunction-vorticity formulations of 2D steady state Navier–Stokes equations. Int. J. Numer. Meth. Fluids 22, 1–9 (1996)CrossRefMATH
18.
Zurück zum Zitat Liao, S.-J., Zhu, S.-P.: Solving the Liouville equation with the general boundary element method approach. Bound. Elem. Tech. XIII, 407–416 (1999) Liao, S.-J., Zhu, S.-P.: Solving the Liouville equation with the general boundary element method approach. Bound. Elem. Tech. XIII, 407–416 (1999)
19.
Zurück zum Zitat Lo, C.F., Lee, H.C., Hui, C.H.: A simple approach for pricing barrier options with time-dependent parameters. Quant. Financ. 3, 98–107 (2003)CrossRefMathSciNet Lo, C.F., Lee, H.C., Hui, C.H.: A simple approach for pricing barrier options with time-dependent parameters. Quant. Financ. 3, 98–107 (2003)CrossRefMathSciNet
21.
Zurück zum Zitat Ortega, J.M., Rheinboldt, W.C.: Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, New York (1970)MATH Ortega, J.M., Rheinboldt, W.C.: Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, New York (1970)MATH
22.
Zurück zum Zitat Park, S.-H., Kim, J.-H.: Homotopy analysis method for option pricing under stochastic volatility. Appl. Math. Lett. 24, 1740–1744 (2011)CrossRefMATHMathSciNet Park, S.-H., Kim, J.-H.: Homotopy analysis method for option pricing under stochastic volatility. Appl. Math. Lett. 24, 1740–1744 (2011)CrossRefMATHMathSciNet
23.
Zurück zum Zitat Rich, D.: The mathematical foundations of barrier option-pricing theory. Adv. Futur. Options Res. 7, 267–311 (1994) Rich, D.: The mathematical foundations of barrier option-pricing theory. Adv. Futur. Options Res. 7, 267–311 (1994)
24.
Zurück zum Zitat Roberts, G.O., Shortland, C.F.: Pricing barrier options with time-dependent coefficients. Math. Financ. 7, 83–93 (1997)CrossRefMATH Roberts, G.O., Shortland, C.F.: Pricing barrier options with time-dependent coefficients. Math. Financ. 7, 83–93 (1997)CrossRefMATH
25.
Zurück zum Zitat Rubinstein, M., Reiner, E.: Breaking down the barriers. RISK 4, 28–35 (1991) Rubinstein, M., Reiner, E.: Breaking down the barriers. RISK 4, 28–35 (1991)
26.
Zurück zum Zitat Zhu, S.-P.: An exact and explicit solution for the valuation of American put options. Quant. Financ. 6(3), 229–242 (2006)CrossRefMATH Zhu, S.-P.: An exact and explicit solution for the valuation of American put options. Quant. Financ. 6(3), 229–242 (2006)CrossRefMATH
27.
Zurück zum Zitat Zhu, S.-P., Chan, L.: An Analytic Formula for Pricing American Options with Regime Switching (2013) [Epub ahead of print] Zhu, S.-P., Chan, L.: An Analytic Formula for Pricing American Options with Regime Switching (2013) [Epub ahead of print]
Metadaten
Titel
An explicit analytic formula for pricing barrier options with regime switching
verfasst von
Leunglung Chan
Song-Ping Zhu
Publikationsdatum
01.01.2015
Verlag
Springer Berlin Heidelberg
Erschienen in
Mathematics and Financial Economics / Ausgabe 1/2015
Print ISSN: 1862-9679
Elektronische ISSN: 1862-9660
DOI
https://doi.org/10.1007/s11579-014-0119-z

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